final cut newbie, can I move sections from timeline into an event?

Okay, in the Browser you basically mark ranges within the source clip, by dragging a selection or by playing the clip and using "I" and "O" to set in and out points. With a range selected, you could "tag" it (similar to creating a subclip). The manual clearly explains this. Perhaps, it's better to say that in the Browser you organize (select and tag) your source media.

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Yes, in order to copy-paste clips between timelines you would need to create another Project. Just above the timeline area in the user interface of FCP is the Project name. The the left and right icons "<" and ">" are arrows that you can use to move between Projects (or you can use command-[ or command-]).

Once you blade your (two hour) source clip in a timeline into multiple clips (if editing in a timeline and not the Browser), you can select each clip and with the "i" (info) inspector pane active you can change the clip name in the inspector, add a Note, etc.

NLE means non-linear editor, in other words, Final Cut Pro, Premiere Pro, AVID Media Composer, or DaVinci Resolve, just to name the more popular ones. Other than Final Cut Pro, the other NLEs use tracks. FCP has its "magnetic timeline". You can drag a clip upwards in FCP to simulate moving it to another track.

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Since you don't have much time, you might want to stick with timeline editing for now. You could group related clips by situating them spatially along the timeline. You could use titles to identify the groups (along with changing the clip names). Once you've reviewed the source and identified which parts you want to use, you can edit those clips to section of the timeline or to another timeline.

This might be helpful (and good to watch again later):

https://www.rippletraining.com/learn-fcp-in-under-60-minutes/

Hope this helps...

P.S. - Tracks are like layers in Photoshop. They let you organize clips in the timeline. The topmost clips in a stack of tracks are visible. Tracks can be used to separate clips by purpose, such as main story, b-roll, VFX, titles, temporary clips, etc. Final Cut Pro uses connected clips and connected storylines in lieu of tracks. The above referenced video should help make this more clear...

You are correct in not really being able to create "sub-clips" in the timeline and move them to an Event...

The way FCP is really designed to work is to organize and tag source clips in the Browser (Event Viewer). You can select ranges in the source clip and tag them with keywords, ratings, and metadata (notes, etc.). You could then create smart collections to organize your selected clips. The user manual (via Help menu) provides a good overview of this. In a simple case, you could "favorite" all of the desired ranges in your original clip, then filter your Browser to just display the favorited ranges. With your tagging/selecting done, you could display only what you want via smart collections (saved searches). You'd then edit what you want into a timeline/Project. This is a very crude overview of the "preferred way" to organize media in FCP. Events are like top-level folders. Keyword and smart collections replace bins (as used in other NLEs) in FCP, for the most part.

"Timeline Editing"

Another option would be to edit your source media in a timeline, removing what you don't want (or moving it to the end of the timeline, for example). You could optionally copy the remaining clips (or move them) to the end of the timeline, grouping them. You could also move clips to become connected clips/storylines as another way to visually "rate" them (like moving them to other tracks in other NLEs). You could then edit your chosen clips to the beginning of the timeline and disable or delete the rest once you're done editing. Alternatively, you could copy-paste your selected clips to another timeline, switching back and forth as you go.

In a pinch (I wouldn't recommend this for "larger" projects — it's definitely a "hack"), you could select your selected/desired clip in the timeline and create a compound clip out of it. The compound clip will show in the source Event. From there you could copy it and paste it into another Event or use that to edit into a new timeline.

Some food for thought...

You can select your clip in the Event Browser. Type the Home key to set the playhead at the beginning. Start playing and watch the clip. To set an in point for a subclip you want to add to the storyline, type Command-Shift-i. To set an outpoint for a subclip, type Command-Shift-o — and just keep setting in and out points as it plays. To speed things up a little bit, type the L key to increase the playback speed. (If you can handle it, type the L key again to increase the speed to 4x.) [You basically just want to get some meaningful part of the clip in the storyline... don't obsess over exact timings.]

When you have all the In/Out points you want, type the E key to add *all* the subclips (in order) to the Storyline.

Once you get everything in the storyline, you can use the trim tools to clean up the clip ends.

To clear the Event browser clip of all in/out points, type Option-X. To make the entire clip a selection, type X.

As an alternative, once you have all the In/Out segments, make sure they're "highlighted" and type the F key to Favorite the subclips. Up at the top of the column where it says "All Clips", select Favorites. All the subclips will appear as separate clips in the Event browser and you can add them individually in any order you like (or you can "select all" and add them to the storyline by typing the E key.)

I find Favoriting to be occasionally a little iffy if I don't watch to see if the green bar (indicator for favorites at the top of the subclip) appears when I type F. It's something you have to be a little more careful of.

HTH